<p>The modelling and analysis of complex stochastic systems with increasingly large data sets, state-spaces and parameters provides major stimulus to research in Bayesian nonparametric methods and Bayesian computation. ...

<p>This thesis focuses on the development of ABC methods for statistical modeling in complex dynamic systems. Motivated by real applications in biology, I propose computational strategies for Bayesian inference in contexts ...

<p>This thesis is about Bayesian approaches for handling multiplicity. It considers three main kinds of multiple-testing scenarios: tests of exchangeable experimental units, tests for variable inclusion in linear regresson ...

<p>Dynamic models, also termed state space models, comprise an extremely rich model class for time series analysis. This dissertation focuses on building state space models for a variety of contexts and computationally ...

<p>We explore the posterior inference available for Bayesian spatial point process models. In the literature, discussion of such models is usually focused on model fitting and rejecting complete spatial randomness, with ...

<p>With the development of modern data collection approaches, researchers may collect hundreds to millions of variables, yet may not need to utilize all explanatory variables available in predictive models. Hence, choosing ...

<p>The first part of the thesis focuses on the development of Bayesian modeling motivated by geophysics applications. In Chapter 2, we model the frequency of pyroclastic flows collected from the Soufriere Hills volcano. ...

<p>Multivariate or high-dimensional data with mixed types are ubiquitous in many fields of studies, including science, engineering, social science, finance, health and medicine, and joint analysis of such data entails both ...

<p>This dissertation is devoted to modeling complex data from the</p><p>Bayesian perspective via constructing priors with latent structures.</p><p>There are three major contexts in which this is done -- strategies for</p><p>the ...

<p>The Bayesian approach to model selection allows for uncertainty in both model specific parameters and in the models themselves. Much of the recent Bayesian model uncertainty literature has focused on defining these ...

<p>Modelling and inference with higher-dimensional variables, including studies in multivariate time series analysis, raise challenges to our ability to ``scale-up'' statistical approaches that involve both modelling and ...

<p>The dissertation focuses on solving some important theoretical and methodological problems associated with Bayesian modeling of infinite dimensional `objects', popularly called nonparametric Bayes. The term `infinite ...

<p>Identifying a lower-dimensional latent space for representation of high-dimensional observations is of significant importance in numerous biomedical and machine learning applications. In many such applications, it is ...

<p>In this thesis, we develop some Bayesian sparse learning methods for high dimensional data analysis. There are two important topics that are related to the idea of sparse learning -- variable selection and factor analysis. ...

<p>This thesis concerns the use of protein structure to improve phylogenetic inference. There has been growing interest in phylogenetics as the number of available DNA and protein sequences continues to grow rapidly and ...

<p>Clustering methods are designed to separate heterogeneous data into groups of similar objects such that objects within a group are similar, and objects in different groups are dissimilar. From the machine learning ...